Math 5710  Introduction to Applied Mathematics
M W F   11:50 am - 12:40 pm     JTB 320
  
                                   Mathematics is the Queen that rules the Universe    

 Text: Gilbert Strang, Introduction to Applied Mathematics, 1986

 Instructor:   Prof. Elena Cherkaev
   Office:   LCB 206        ph: 801-581-7315  
        email:    elena@math.utah.edu

   Office hours: W   1-2 pm and by appointment
 
Class webpage:  http://www.math.utah.edu/~elena/M5710/5710.html

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  ***  Midterm 1 - Oct 20  ***  test will cover material including section 2.4
  ***    practice test
  ***  Midterm 2 - Nov 22  ***  test will cover material in sections 3.1- 3.4
   Sample problems:   3.1: #  1, 5-6, 15;  3.2: #  1-3,  6-7,  10-11;   3.3: #  11-13;  3.4: #  2, 5
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Assigned Homework Problems 
Show all work (No work shown => No credit given)
 
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Hw1 (due Sept. 6):   1.4.10,   1.4.11,   1.4.15,   1.4.2
                 sect. 1.3:  ##  8,  11,  12,  20;   sect. 1.4:  ##  2, 6, 7, 8
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Hw2 (due Sept. 20):  sect. 2.1:  #  2, 5;   sect. 2.2:  #  1, 3
                           sect. 2.2:  #  7, 10, 11, 12, 14
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Hw3 (due Oct. 4/6):  sect. 2.3:  #  1, 2,  3, 9, 11
                                     sect. 2.4:  #  2, 5, 7, 10, 11, 12
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Hw4 (due Oct. 18):  sect. 3.1:  #  1, 4, 5,  12, 13      delta-function
                                 sect. 3.1:   #   6, 15, 16.    Sect. 3.2:  #  1, 2
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Hw5 (due Nov. 3):  sect. 3.2:  #  3, 4, 6,  7, 8,  10, 11
                                      sect.  3.3:  #  1,  2,  6
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Hw6 (due Nov. 15):  sect.  3.3:  #  7,  8,  9,  11,  12,  13,  14,  16,  17, 19 ---------------------------------------------------------------------------------------------
Hw7 (due Nov. 29):  sect.  3.4:  # 2, 3, 4, 5, 8, 10,  18, 19
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Hw8 (due Dec. 13):  sect.  3.4:  # 23,  24,  34
                                        sect.  3.5:  # 2,  3,  4,  7,  8,  15, 23
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Class Log  
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Aug 21-27: We start with a model of a spring/mass chain (sect. 1.4, Ex. 2, pp. 40-41) to continue next time and talk about a fundamental principle of the minimum of the potential energy (sect. 1.4).  We will also discuss least squares solutions to linear problems.

Aug 28-Sept 1: M, F - Electric networks. W - No lecture. Refresh linear algebra (ch. 1).

Sept 4-8: W, F - Lagrange multipliers (sect. 2.2)

Sept 11-15:  We discuss duality and its applications

Sept 18-22:  We will talk about electrical networks and minimum principles (sect. 2.3) and then continue with networks of elastic bars or trusses (sect. 2.4)

Sept 25-29:  We discuss structures in equilibrium (sect. 2.4). A particular example of such a structure is a truss made of elastic bars connected by hinges. We also start to talk about equilibrium in the continuous case for a one-dimensional problem (sect. 3.1).

Oct 2-6:  We discuss equilibrium in continuous one-dimensional problems, Sturm- Liouville problems, regular and singular perturbations (sect. 3.1).

Oct 9-13:  Fall break

Oct 16-20:  We talk about delta function and discuss differential equations of equilibrium (sect. 3.2).

Oct 23-27:  We continue to discuss equations of equilibrium, minimum principles, duality for one-dimensional problems such as stretching or bending of a beam (sect. 3.2).

Oct 30-Nov 3: This week we discuss two-dimensional Laplace's equation (section 3.3)  and potential or irrotational flows. 

Nov 6-10:  We start to discuss three-dimensional problems, cross-product, curl, and relations between curl, grad, and div operators (sect. 3.4).

Nov 13-22:  Continue with three-dimensional problems, Maxwell's equations (sect. 3.4).

Nov 27-Dec 1:  We discussion of the Maxwell's equations and three-dimensional flows (sect. 3.4). We also start to talk about solids (sect. 3.5).

Dec 4-6:  Equilibrium of solids and fluids (sect. 3.5).
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Course description: The course gives an overview of methods, problems, and models of applied mathematics, emphasizing parallels between continuous and discrete approaches. We will see how differential equations and matrix equations reinforce each other and go in parallel. "To see the cooperation between calculus and linear algebra is to see one of the best parts of modern applied mathematics." /from the Preface of the textbook/   

    Optimality and duality is another focus of the course (and another best part of modern applied mathematics), which expresses itself as a fundamental principle of energy minimization (or stationarity of the energy). This principle governs all the processes in the world, and we will see mathematical justification of that through the same mathematical framework held for all the problems and topics discussed in the course.
    Particular covered topics include optimization and duality, partial differential equations (potential flows, electricity and magnetism, equilibrium of fluids and solids, heat equation versus wave equation),  ordinary differential equations (stability, chaos and fractals, nonlinear conservation laws), networks (electric, mechanic, social, internet) and transportation problem. 

About the textbook: Renowned mathematician Gilbert Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving. This is an ideal book (beloved by many readers) for a first course on applied mathematics and a reference for more advanced applied mathematicians. The only prerequisite is a basic course in linear algebra. /Google books/
Table of Contents:
  http://www-math.mit.edu/~gs/books/itam_toc.html

Prerequisites:  Calculus, Linear Algebra, and Differential Equations.

Exams:  There will be two midterms, project, and a final exam.

Final: Wednesday, December 13, 2017, 10:30 am – 12:30 pm

Grading: The grade will be based on the homework (20%) and project and the exams (80%). You are welcome to work on the homework problems together with other students, but you have to write your own solutions. 

Holidays:   Labor Day holiday:     Monday, September 4;   
                     Thanksgiving break:  Thurs.-Fri., Nov. 23-24.
Fall break:   October 8-15.

ADA: The "American with Disabilities Act" requires that reasonable accommodations be made for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodation for the course.